The University of Michigan Combinatorics Seminar
Winter 2004
April 16, 4:10-5:00, 3866 East Hall

Convex ear decompositions

Edward Swartz

Cornell University


Spaces with convex ear decompositions were introduced by Chari. A simplicial complex has a convex ear decomposition if it can be built by starting with the boundary of a convex polytope, and then attaching balls of the same dimension which are subcomplexes of (possibly other) convex polytopes. Examples include matroid complexes, order complexes of geometric lattices and spherical buildings. The h-vectors of these spaces satisfy a number of inequalities similar to those suggested by the g-theorem for convex polytopes. These inequalities lead to a number of interesting combinatorial problems.

This talk will be preceded by a VIGRE pre-talk on "Why am I counting faces?"

Pre-talk abstract: The Euler characteristic is the best known example of the value of counting the faces of a simplicial complex. We will give several examples of applications of face counts to other problems including network reliability, real and complex hyperplane arrangements, and graph coloring.